This course discusses single neuron modeling, including molecular models of
channels and channel gating, Hodgkin-Huxley style models of membrane currents, non-linear
dynamics as a way of understanding membrane excitability, neural integration
through cable theory, and network computation. The goal of the course is to
understand how neurons work as biological computing elements and also to give
students experience with modeling techniques as applied to complex biological
The course meets Mondays, Tuesdays, Wednesdays, and Fridays from 9:00-10:00
a.m. on the Homewood campus. The MWF classes are lectures and will be held in Hodson 311. The Tuesday classes are recitations held in
Hodson 301, where homework will be discussed and help with questions provided;
Tuesday recitation is required for undergraduates and optional for graduate
students. The course is taught by Eric Young, 505 Traylor at the Medical School,
telephone 410-955-3164 (firstname.lastname@example.org); the T.A. is Kristin Hageman, telephone
(609) 651-7936 (email@example.com). TA office hours will be on
Wednesdays from 10AM-12PM in Clark 110 (if no one shows up by 10:30AM
office hours will be cancelled for the day unless a prior appointment has been
made). The prerequisites are mathematics through linear algebra and
differential equations and an introduction to neuroscience (e.g. 580.422,
080.205, or 080.304); introductory signal and system theory (e.g. 580.222 or
520.213-214) is helpful.
There is no required text, although Biophysics of Computation by C. Koch is
an excellent book that covers most of the material in the course. Foundations
of Cellular Neurophysiology by D. Johnston and S. Wu covers some of the
material in a more elementary fashion and P. Dayan and L.F. Abbott Theoretical
Neuroscience provides a more modern view of some topics. Several chapters from
Methods in Neuronal Modeling (2nd ed.) edited by C. Koch and I. Segev will be used. An excellent and comprehensive book on
membrane physiology is Ionic Channels of Excitable Membranes, (3rd ed.) by B. Hille. This book covers ion channels in more depth than
those above; it is required reading for anyone seriously interested in this
subject. Additional references include the following: G.M. Shepherd, The
Synaptic Organization of the Brain (4th ed.) is a good introduction to neural
systems for persons with no previous experience. S.H. Strogatz
Nonlinear Dynamics and Chaos cover aspects of nonlinear dynamics and network
theory that will be discussed in the course; some material from H.R. Wilson,
Spikes Decisions and Actions will also be used. The book Dynamical Systems in
Neuroscience by E.M. Izhikevich provides a useful
view of 2nd-order nonlinear systems of the type used in neuroscience. A good
overview of network theory is J. Hertz, A Krogh, and R.G. Palmer, Introduction
to the Theory of Neural Computation. Finally, J.J.B. Jack, D. Noble, and R.W. Tsien, Electric Current Flow in Excitable Cells contains
detailed discussions of older work, especially useful for cable theory. All of
these are on reserve in Eisenhower library.
Weekly homework assignments will be given. Solutions should be handed in
during class on the due date and will be graded. Two computer modeling projects
will be assigned during the term. The grade for graduate students will be based
on the midterm (20%), final (30%), the modeling projects (40%), and the
homework (10%). Undergraduate's grades will be based on the midterm (30%), first
modeling project (30%), final (30%), and homework (10%). Students are
encouraged to discuss homework problems with colleagues, but the final product
that is handed in should be the student's own work. Modeling projects must be
done individually. A conscientious homework record will contribute to raising
Course schedule Updated August 19, 2013
Lectures are MWF 9-10 in Hodson
311. Parentheses indicates no class meeting on that
Sep. 4, 6 - Introduction; review of neurophysiology and thermodynamics.
9, 11, 13 - Equilibria, electrodiffusion I-V relationships; cellular steady state. Biological membranes, ion transporters, channels.
16, 18, 20 - Kcsa and similar channels. Barrier models of channel permeation. Kcsa permeation model.
23, 25, 27 - Transporter models, voltage clamp analysis, gating; Hodgkin-Huxley and similar models.
Sep. 30, Oct. 2, 4 - Phase-plane analysis of nonlinear systems; model reduction, linearization; classification of behavior near equilibrium points
7, 9, 11 - Simulation methods; limit cycles; bifurcations.
(14), 15, 16, 18 - Bursting; role of calcium; varieties of channels; (Class on the 14th is moved to the 15th for fall break). Bursting neurons, corticothalamic neurons; regulation of ion channel density.
MIDTERM EXAM OCT 18, 2013
21, 23, 25 - Synaptic transmission and neuromodulation. Dendritic trees, distribution of inputs on dendrites. Cable equation for dendritic trees.
28, 30, Nov. 1 - Solutions to the cable equation; finite cylinders.
FIRST MODELING PROJECT DUE Oct 30, 5:00 P.M.
Nov. 4, 6, 8 - Transfer functions in dendritic trees; Equivalent cylinder.
11, 13, 15 - Real dendritic trees, synaptic coupling to the soma, arrangement of synapses, subunits.
18, 20, 22 - Spines and calcium. Plasticity; neural integration.
25, (27, 29) - feedforward neural networks. (No class Nov. 27, 29 for Thanksgiving vacation)
Dec.2, 4, 6 - Network learning rules; Hopfield network; Liapunov functions and the Cohen-Grossberg theorem.
FINAL EXAM DEC 14, 2013-9:00 A.M.-Noon in Hodson 311
SECOND MODELING PROJECT DUE DEC 20, 5:00 P.M.
Homework assignments will be given weekly, and are generally due on Fridays by the end of class. They can be submitted in class or dropped off to the TA (notify TA if doing so). Homework will not be accepted after solutions are posted. The links below will return pdf files of the homework sets and solutions. The pdf files can be viewed with the free Adobe Acrobat Reader. Solution sets will be available for downloading after the due-date of the homework.
Other relevant notes
Two computer modeling projects will be assigned. All work on the modeling projects must be done individually.
Due October 30, 2013 by 5:00 P.M.
Due December 20, 2013 by 5:00 P.M.
Copies of previous midterms and finals are posted below, along with solutions.